Remark 3.1 The simplest example of a symmetric spherical order is \(\mathcal {A}= \mbox{\emph {End}}_E(\mathcal {F})\) , where \(\mathcal {F}\)  is a simple vector bundle on \(E\)  of rank \(n\)  and degree \(d\) . It follows from [1]}, [2]}, [3]} that such \(\mathcal {F}\)  exists if and only if \(n\)  and \(d\)  are coprime and the sheaf of algebras \(\mathcal {A}= \mathcal {A}_{(n, d)} = \mbox{\emph {End}}_E(\mathcal {F})\)  does not depend on the choice of \(\mathcal {F}\) . Moreover, according to [4]}, any symmetric spherical order on an elliptic curve \(E\)  is isomorphic to \(\mathcal {A}_{(n, d)}\)  for some \(0 < d < n\)  mutually prime.

